From the work of King [1]}, Ito–Nakajima [2]}, and Craw [3]} one can reinterpret \(G\) -Hilb as a moduli space of quiver representations. The quiver in question is the McKay quiver with vertices indexed by irreducible representations of \(G\)  and the number of arrows between \(\rho \)  and \(\rho ^{\prime }\)  defined to be
\(\operatorname{dim}\operatorname{Hom}_G(\rho ^{\prime }\otimes \rho _{\text{std}},\rho ),\) 
